---
title: "Lines and their rules: cheat sheet"
subtitle: "Linear relations"
---

# Lines and their rules

> The words and methods from this unit, with an example of each.

:::keep-together

**gradient**: $m$, the number in front of $x$: one step right, the line goes up $m$ (down when $m$ is negative). A bigger $m$ is steeper; $m = 0$ is flat.

$$y = \mathbf{3}x + 1$$

_y = 3x + 1: one step right, up 3_

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:::keep-together

**y-intercept**: $c$, the number on its own: where the line crosses the $y$-axis (at $x = 0$). Changing $c$ moves the line up or down without changing its steepness.

$$y = 2x + \mathbf{4}$$

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:::keep-together

**parallel lines**: The same $m$ gives the same steepness, so the lines never meet. $y = 2x + 4$ is $y = 2x + 1$ moved up 3.

$$y = 2x + 1 \quad y = 2x + 4$$

_y = 2x + 1 and y = 2x + 4: same m, so parallel_

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:::keep-together

**vertical and horizontal lines**: One letter: every point on $x = 3$ has $x = 3$ (a vertical line); every point on $y = -2$ has $y = -2$ (horizontal).

$$x = 3 \quad y = -2$$

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:::keep-together

**inequality region**: Draw the boundary $y = 2x + 1$: dashed for $<$ and $>$, solid for $\le$ and $\ge$. Test a point such as $(0, 0)$: true, shade its side; false, the other side.

$$y < 2x + 1$$

_y < 2x + 1: below the dashed line, including (0, 0)_

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